Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

TL;DR

This paper introduces a frequency domain Fourier-based method for parametrizing memory kernels in linear generalized Langevin equations from molecular dynamics data, improving accuracy over traditional time-domain methods.

Contribution

It develops a novel Fourier-based parametrization technique for the memory kernel in GLEs, surpassing existing time-domain approaches and clarifies limitations of the rigid bond method.

Findings

Fourier-based parametrization outperforms time-domain methods.

Rigid bond method is generally inappropriate for GLE parametrization.

Rigid bond approach underestimates relaxation times unless specific conditions are met.

Abstract

Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation (GLE), which can be rigorously derived by means of a linear projection (LP) technique. Within this framework a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here we discuss that this task is most naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic underestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.